Stream-based accelerator processing of computational graphs

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for receiving, by a computational graph system, a request to process a computational graph; obtaining data representing a subgraph of the computational graph, the computational graph comprising a plurality of nodes and directed edges, wherein each node represents a respective operation, wherein each directed edge connects a respective first node to a respective second node, the subgraph assigned to a first device by a placer in the computational graph system; determining that the first device comprises a hardware accelerator having a plurality of streams; in response to determining, generating instructions that when executed by the first device cause the first device to: assign the operation represented by each node in the subgraph to a respective stream; and perform the operations represented by the nodes in the subgraph in accordance with the assignment.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. § 119(e) of thefiling date of U.S. Patent Application No. 62/247,703, entitledPROCESSING COMPUTATIONAL GRAPHS, which was filed on Oct. 28, 2015, andclaims the benefit of U.S. Patent Application No. 62/253,046, entitledPROCESSING COMPUTATIONAL GRAPHS, filed on Nov. 9, 2015. The disclosuresof the prior applications are considered part of and are incorporated byreference in the disclosure of this application.

BACKGROUND

This specification relates to processing computational graphsrepresenting neural networks using an accelerator device, e.g., agraphical processing unit (GPU).

Neural networks are machine learning models that employ one or morelayers of models to generate an output, e.g., one or moreclassifications, for a received input. Some neural networks include oneor more hidden layers in addition to an output layer. The output of eachhidden layer is used as input to the next layer in the network, i.e.,the next hidden layer or the output layer of the network. Each layer ofthe network generates an output from a received input in accordance withcurrent values of a respective set of parameters for the layer.

In systems that exist, the operations of computational graphs can beprocessed by an individual device. In some implementations, the deviceis a GPU. The device can have a processor that performs operations,e.g., generating outputs at a layer from inputs, and stores outputs fromthe operations in memory. Due to the large number and size of operationsgenerally required to generate the outputs in the computational graph,one device can take a significant amount of time to process theoperations of the graph.

SUMMARY

In general, this specification describes a system for processingsubgraphs of a computational graph using a stream-based acceleratordevice, e.g., a GPU.

In general, one innovative aspect of the subject matter described inthis specification can be embodied in methods that include the actionsof receiving, by a computational graph system, a request to process acomputational graph; obtaining data representing a subgraph of thecomputational graph, the computational graph comprising a plurality ofnodes and directed edges, wherein each node represents a respectiveoperation, wherein each directed edge connects a respective first nodeto a respective second node that represents an operation that receives,as input, an output of an operation represented by the respective firstnode, the subgraph assigned to a first device by a placer in thecomputational graph system; determining that the first device comprisesa graphical processing unit having a plurality of streams; in responseto determining that the first device comprises a graphical processingunit having a plurality of streams, generating instructions that whenexecuted by the first device cause the first device to: assign theoperation represented by each node in the subgraph to a respectivestream in the plurality of streams of the graphical processing unit; andperform the operations represented by the nodes in the subgraph inaccordance with the assignment; and providing the instructions and thedata to the first device.

Implementations can include one or more of the following features. Therequest specifies identifying one or more particular outputs from one ormore respective nodes in the subgraph, further comprising: receiving,from the first device, the one or more particular outputs; and providingthe one or more particular outputs to the client. The instructionsfurther cause the first device to store the one or more particularoutputs in memory of the first device. The operations for the subgraphcomprise partial inference or training computations for a neuralnetwork. Analyzing the subgraph to identify a group of nodes in thesubgraph in a chain structure; wherein the instructions cause the firstdevice to assign the group of nodes to one stream. The assigningcomprises: analyzing the subgraph to identify a first node in thesubgraph has a plurality of directed edges as outputs; wherein theinstructions cause the first device to assign, for each of the directededges, a node to which the directed edge points to a unique stream ofthe graphical processing unit. The instructions cause the first deviceto determine, for each node, a respective amount of memory resources inthe graphical processing unit consumed by the operation represented bythe node based on the directed edges to the node, wherein the assigningis based at least on the respective amount of memory resources. Theinstructions cause the first device to determine a particular operationrepresented by a node has finished at a particular stream; in responseto determining the particular operation has finished: determine a firstamount of memory consumed by the particular operation that will befreed; determine, for each of a group of unassigned nodes, a respectiveestimated amount of memory consumed by the unassigned node; determine,from the group of unassigned nodes, a first unassigned node with theestimated amount of memory that maximizes usage of the first amount ofmemory; and assign an operation represented by the first unassigned nodeto the particular stream.

Another innovative aspect includes the actions of receiving, by agraphical processing unit having a plurality of streams, datarepresenting a subgraph of the computational graph, the computationalgraph comprising a plurality of nodes and directed edges, wherein eachnode represents a respective operation, wherein each directed edgeconnects a respective first node to a respective second node thatrepresents an operation that receives, as input, an output of anoperation represented by the respective first node, the subgraphassigned to a graphical processing unit by a placer in a computationalgraph system; assigning the operation represented by each node in thesubgraph to a respective stream in the plurality of streams of thegraphical processing unit; and performing the operations represented bythe nodes in the subgraph in accordance with the assignment.

Implementations can include one or more of the following features.Receiving a request identifying one or more particular outputs from oneor more respective nodes in the subgraph; and providing the one or moreparticular outputs to the client. Receiving data identifying a group ofnodes in the subgraph in a chain structure; and assigning the group ofnodes to one stream. The assigning comprises: receiving data identifyinga first node in the subgraph having a plurality of directed edges asoutputs; and assigning, for each of the directed edges, a node to whichthe directed edge points to a unique stream of the graphical processingunit. Determining, for each node, a respective amount of memoryresources in the graphical processing unit consumed by the operationrepresented by the node based on the directed edges to the node, whereinthe assigning is based at least on the respective amount of memoryresources. Determining a particular operation represented by a node hasfinished at a particular stream; in response to determining theparticular operation has finished, determining a first amount of memoryconsumed by the particular operation that will be freed; determining,for each of a group of unassigned nodes, a respective estimated amountof memory consumed by the unassigned node; determining, from the groupof unassigned nodes, a first unassigned node with the estimated amountof memory that maximizes usage of the first amount of memory; andassigning an operation represented by the first unassigned node to theparticular stream.

Particular embodiments of the subject matter described in thisspecification can be implemented so as to realize one or more of thefollowing advantages. Operations, e.g., an operation to generate aninference from an input, of a neural network can be represented as acomputational graph of nodes and directed edges. A system processes thiscomputational graph representation to efficiently perform theoperations. The system achieves this efficiency because thecomputational graph has multiple streams. Using multiple streams canallow logically independent operations to be reordered or executedconcurrently. When the system has a goal of lowering end-to-end latencyfor a whole computation, the example system may reorder logicallyindependent operations. When the system has a goal to achieve higherthroughput, the example system may execute operations simultaneously.The computational graph can be more easily partitioned for paralleloperations than the conventional representation. By way of illustration,subgraphs of the computational graph can be assigned to unique devices,each of which performs operations in the respective subgraph, to reducean overall time required to perform operations of the neural network.

A device to which a subgraph is assigned can be a GPU. The subgraph canbe partitioned into multiple streams of the GPU to more efficientlyperform the operations of the subgraph. The details of one or moreembodiments of the subject matter of this specification are set forth inthe accompanying drawings and the description below. Other features,aspects, and advantages of the subject matter will become apparent fromthe description, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example computational graph system fordistributing operations for neural networks represented as computationalgraphs.

FIG. 2 is a flow diagram of an example process for processing a subgraphof a computational graph using a GPU.

FIG. 3 illustrates an example subgraph of a computational graph beingprocessed by a GPU.

FIG. 4 is a flow diagram of an example process for assigning nodes tostreams.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification generally describes a computational graph system thatperforms operations represented by a computational graph in adistributed manner.

The computational graph includes nodes connected by directed edges. Eachnode in the computational graph represents an operation. An incomingedge to a node represents a flow of an input into the node, i.e., aninput to the operation represented by the node. An outgoing edge from anode represents a flow of an output of the operation represented by thenode to be used as an input to an operation represented by another node.Thus, a directed edge connecting a first node in the graph to a secondnode in the graph indicates that an output generated by the operationrepresented by the first node is used as an input to the operationrepresented by the second node.

Generally, the input and outputs flowing along directed edges in thecomputational graph are tensors. A tensor is a multidimensional array ofnumeric values or other values, e.g., strings, having a specific orderthat corresponds to the dimensionality of the array. For example, ascalar value is a 0th-order tensor, a vector of numeric values is a1st-order tensor, and a matrix is a 2nd-order tensor.

In some implementations, the operations represented in the computationalgraph are neural network operations or operations for a different kindof machine learning model. A neural network is a machine learning modelthat employs one or more layers of nonlinear units to predict an outputfor a received input. Some neural networks are deep neural networks thatinclude one or more hidden layers in addition to an output layer. Theoutput of each hidden layer is used as input to another layer in thenetwork, i.e., another hidden layer, the output layer, or both. Somelayers of the network generate an output from a received input inaccordance with current values of a respective set of parameters, whileother layers of the network may not have parameters.

For example, the operations represented by the computational graph maybe operations necessary for the neural network to compute an inference,i.e., to process an input through the layers of the neural network togenerate a neural network output for the input. As another example, theoperations represented by the computational graph may be operationsnecessary to train the neural network by performing a neural networktraining procedure to adjust the values of the parameters of the neuralnetwork, e.g., to determine trained values of the parameters frominitial values of the parameters. In some cases, e.g., during trainingof the neural network, the operations represented by the computationalgraph can include operations performed by multiple replicas of theneural network.

By way of illustration, a neural network layer that receives an inputfrom a previous layer can use a parameter matrix to perform a matrixmultiplication between the parameter matrix and the input. In somecases, this matrix multiplication can be represented as multiple nodesin the computational graph. For example, a matrix multiplication can bedivided into multiple multiplication and addition operations, and eachoperation can be represented by a different node in the computationalgraph. The operation represented by each node can generate a respectiveoutput, which flows on a directed edge to a subsequent node. After theoperation represented by a final node generates a result of the matrixmultiplication, the result flows, on a directed edge, to another node.The result is equivalent to an output of the neural network layer thatperforms the matrix multiplication.

In some other cases, the matrix multiplication is represented as onenode in the graph. The operations represented by the node can receive,as inputs, an input tensor on a first directed edge and a weight tensor,e.g., a parameter matrix, on a second directed edge. In someimplementations, the weight tensor is associated with the sharedpersistent state of the model. The node can process, e.g., perform amatrix multiplication of, the input and weight tensors to output, on athird directed edge, an output tensor, which is equivalent to an outputof the neural network layer.

Other neural network operations that may be represented by nodes in thecomputational graph include other mathematical operations, e.g.,subtraction, division, and gradient computations; array operations,e.g., concatenate, splice, split, or rank; and neural network buildingblock operations, e.g., SoftMax, Sigmoid, rectified linear unit (ReLU),or convolutions.

Representing a neural network as a computational graph provides for aflexible and granular way to efficiently implement the neural network,especially if the operations for the neural network are distributedacross multiple devices with different hardware profiles.

FIG. 1 illustrates an example computational graph system 100 fordistributing operations for neural networks represented as computationalgraphs. The system 100 is an example of a system implemented as computerprograms on one or more computers in one or more locations, in which thesystems, components, and techniques described below can be implemented.

A user of a client 102 can request actions be performed on acomputational graph representing a neural network. For example, a clientcan register a graph with the session manager, feed data input into thegraph, or evaluate one or more of the outputs of a graph. The client 102can be an application running on a computer.

As part of the request, the client 102 provides data identifying acomputational graph to the system 100 and specifies types of actions tobe performed on the computational graph.

For example, the request can identify a computational graph representingan inference for a particular neural network and can identify an inputon which the inference should be performed.

As another example, the request can identify a computational graphrepresenting a training procedure for a particular neural network andcan identify an input, such as training data, on which the trainingshould be performed. In this example, when receiving a request toprocess a computation graph representing a training procedure, thesystem 100 can determine modified values for parameters for one or moreedges of the computational graph, e.g., using conventionalbackpropagation or other neural network training techniques. The system100 can store the modified parameters in memory of a device, and anexecutor 106 can retrieve and store, at the system 100, addresses of themodified weights. Upon further requests from the client 102 forinference, training, or other operations requiring the modified weights,the system 100 can access the modified weights using the addresses.

In some cases, the request may specify a response that should betransmitted in response to the request. For example, for a neuralnetwork training request, the client 102 can request an indication thatthe requested neural network training operations have been completedand, optionally, trained values of the parameters of the neural networkor an indication of a memory location from which the trained values canbe accessed by the client 102. As another example, for a neural networkinference request, the client 102 can request output values thatrepresent an inference operation from one or more particular nodes ofthe computational graph.

The system 100 performs the operations to generate the particular outputby partitioning the operations represented by the computational graphacross multiple devices 116-122. The system 100 partitions theoperations to the multiple devices 116-122 over a data communicationnetwork 114, e.g., local area network (LAN) or wide area network (WAN).The devices 116-122 perform the operations and, if applicable, return arespective output or indication to the system 100, which can return therequested output or indication to the client 102.

Any devices performing neural network operations, e.g., devices 116-122,can include a memory, e.g., a random access memory (RAM), for storinginstructions and data and a processor for executing stored instructions.Generally, each device is a hardware resource that performs operationsindependent of other devices. For example, each device can have its ownprocessing unit. The devices can be Graphical Processing Units (GPUs),Central Processing Units (CPUs), or other accelerators. By way ofillustration, one machine can host one or more devices, e.g., multipleCPUs and GPUs.

Each device can also have a respective computational capability. Thatis, devices can have different amount of memories, processing speed, orother architectural characteristics. Thus, some devices can performoperations that other devices cannot. For example, some operationsrequire a certain amount of memory that only particular devices have, orsome devices are configured to only perform a particular type ofoperation, e.g., inference operations.

A session manager 104 in the system 100 receives a request from theclient 102 to start a session during which operations of thecomputational graph are performed. The session manager 104 manages theset of devices, e.g., devices 116-122, that can perform operations ofthe computational graph, and can provide a placer 108 with the set ofdevices that are available to perform operations.

The placer 108 determines, for each operation to be performed in thecomputational graph, a respective target device, e.g., device 116, thatperforms the operation, and in some implementations, a time for therespective target device to perform the operation. The placer 108performs optimal device assignment by knowing how long an operation willtake on each available device given the size of the input data. Theplacer 108 obtains the estimate of processing time using measurements orpredictive performance models. Some operations can be performed inparallel while other operations require prior operations in thecomputational graph to be completed, e.g., the other operations process,as inputs, outputs of the prior operations.

After the devices perform the operations allocated by the placer 108 togenerate outputs, the executor 106 can retrieve the outputs. Theexecutor 106 can generate an appropriate response to the request, e.g.,an output or an indication that the processing has been completed. Then,the executor 106 can return the response to the client 102. AlthoughFIG. 1 illustrates one executor 106, in one implementation, there is anexecutor per device. This executor issues operations to the device whenthey become runnable (i.e., all of their inputs have been computed).This implementation also has a graph manager that partitions a graph torun on multiple devices by invoking the placer 108 and creates thenecessary executors.

The session manager 104 also provides sets of operations to be performedin the computational graph to the executor 106. The executor 106periodically retrieves runtime statistics from the devices 116-122related to graph execution of operations. The executor 106 provides theruntime statistics to the placer 108, which can re-optimize placementand scheduling of further operations.

FIG. 2 is a flow diagram of an example process 200 for processing asubgraph of a computational graph using a GPU. For convenience, theprocess 200 will be described as being performed by a system of one ormore computers located in one or more locations. For example, acomputational graph system, e.g., the computational graph system 100 ofFIG. 1, appropriately programmed, can perform the process 200.

The system receives a request from a client to process a computationalgraph (step 202). For example, the request can be a request to perform aneural network inference represented by the computational graph on aspecified input, a request to perform neural network training operationsrepresented by the computational graph on a specified set of trainingdata, or a request to perform other neural network operationsrepresented by the computational graph, as described above withreference to FIG. 1.

In some cases, a computational graph is sent with the request from theclient. In other cases, the request identifies the computational graphand the system retrieves the data representing the identified graph frommemory.

The system can partition the computational graph into multiplesubgraphs. In some implementations, the subgraphs are specified by theclient sending the request, and the system partitions the computationalgraph according to the specifications. In some other implementations,the system partitions the computational graph such that each subgraphrequires a similar amount of resources for performing operationscompared to the other subgraphs.

The system can assign each subgraph to an available device, e.g., usingplacer 108 of FIG. 1.

The system obtains data representing a particular subgraph of thecomputational graph (step 204) from the partitioned computational graph.The data can be obtained from a database or memory of the system. By wayof illustration, operations of the particular subgraph represent partialinference or training computations.

The system determines that a device to which the subgraph is assigned isa graphical processing unit or other hardware accelerator device havingmultiple streams (step 206). By way of illustration, the system canassess whether the device is a GPU with multiple streams by requesting atype of the device from a resource manager that manages devices to beassigned to the computational graph. Each stream is an independenthardware queue whose operations are processed in order.

The system generates instructions that, when executed by the device,cause the device to perform particular operations (step 208). Inparticular, the instructions cause the device to assign the operationrepresented by each node in the subgraph to a respective stream of thedevice.

An example system may assign computations of some hardware acceleratorsto streams in a particular way (e.g., if one operation executes onstream A, then a later, related operation must also execute on streamA.) For example, a first operation may be stateful and execute on streamA. By executing, the first operation may change the internal state ofthe hardware in a way that must happen before a second operationexecutes. The second operation may then execute on stream A after thefirst operation is complete.

In some implementations, two internal hardware resources cannot be usedsimultaneously and therefore need to be serialized.

Generally, the device assigns operations that do not depend on eachother to different streams. By assigning operations that do not dependon each other to different streams, the hardware does not need to knowhow long an operation will take and can choose from a number ofavailable operations to execute the first one that is ready to executewithout expensive host intervention.

The instructions also cause the device to perform the operationsrepresented by the nodes in the subgraph in accordance with theassignment. When operations are assigned to a particular stream, theoperations are queued. The device can perform operations in afirst-in-first-out (FIFO) manner. Thus, if the device only has onestream, the operations assigned to the device are performed serially. Ifthe device has multiple streams, the operations in different streams canbe performed in parallel and reordered with respect to each other, whilethe operations within a given stream are performed serially. Performingoperations using multiple streams decreases a total time to perform theoperations of the subgraph. This is described further below withreference to FIGS. 3 and 4.

The system provides the instructions and the data to the device (step210). In some implementations, the system sends the device a request tostart the operations. The device receives the request and in response,executes the instructions received from the system.

FIG. 3 illustrates an example subgraph 316 of a computational graphbeing processed by an Accelerator 302. The subgraph 316 has nodes308-314, each of which represent an operation to be performed by theAccelerator 302. A computational graph system, e.g., the system 100 ofFIG. 1, assigned the subgraph 316 to the Accelerator 302.

The Accelerator 302 has two streams 304 and 306. The streams shareutilization of the Accelerator 302. In GPU, streams may be symmetric,meaning that all operations can be performed on any stream. Thissymmetry may not be available of all accelerator devices. For example,on specific accelerator devices certain streams must be used to performoperations that copy data between host and device memory.

The computational graph system can analyze the subgraph 316 to determinehow the subgraph 316 is assigned to the multiple streams 304 and 306. Insome implementations, the system generates instructions that causes theAccelerator 302 to assign the nodes of the subgraph 316 in a way thatminimizes the number of times a directed edge connects to differentstreams. There may be a performance cost to enforcing dependenciesbetween streams. Ordering instructions has some overhead cost. Everyordering dependency reduces the number of possible execution orderingsavailable to the device, reducing scheduling flexibility. Each time adirected edge from a first stream connects to a second stream, thesecond stream waits for the operation with the directed edge from thefirst stream to the second stream to complete processing. Waiting cancause the second stream to remain idle, which causes the GPU to beinefficiently utilized.

In some implementations, the system generates instructions that causesthe Accelerator 302 to assign the nodes of the subgraph 316 based oncharacteristics of the Accelerator 302. For example, the Accelerator 302has a fixed number of streams, i.e., streams 304 and 306. The system canassign the nodes so each stream will be similarly utilized by theAccelerator 302. For accelerators that are GPUs, all streams share asingle large pool of threads.

Some streams also perform particular operations that other streams donot. For example, stream 306 can perform direct memory access (DMA)operations while stream 304 does not. Thus, the system can analyze eachnode to determine a type of operation represented by the node, and thesystem can assign the node to a stream that is able to perform the typeof operation. In GPUs, the main congested resources are DMA engines thatcopy data between hosts and device memory. DMA engines can be used byany stream. If one stream is executing a DMA operation, the streamcannot simultaneously execute a computation. An example system thereforeensures that at least one other stream has some compute work to executeat the same time. The system can analyze the subgraph to identify, andthus, generate instructions that causes a software module or driver thatmanages assigning operations to assign nodes by following two generalrules. First, the system tries to assign nodes arranged in a chainstructure to the same stream. Nodes in a chain structure are nodes thatare connected to each other by following one directed edge from node tonode. Thus, a node in the chain must wait for operations at previousnodes in the chain to finish computing before computing its ownoperation. Assigning chains of nodes is not always possible sincebranching and merging occur in the graph, e.g., from shared inputvariables or common subexpressions.

Second, the system can choose to generate instructions that cause theAccelerator 302 to assign multiple nodes that each receive input fromone node to unique streams. That is, if a first node has multipleoutputs to multiple different nodes, the system assigns each of thedifferent nodes to a unique stream. Each of the different nodes do nothave data dependence on any of the other different nodes, and therefore,improve efficiency when operating on disjoint streams.

By way of illustration, the Accelerator 302 receives the subgraph 316.The instructions received by the system cause the Accelerator 302 toassign the initial node 308 to a first stream 306. The initial node 308has two outputs—one directed edge to node 310 and one directed edge tonode 314. Therefore, using the second rule, the instructions cause theAccelerator 302 to assigns nodes 310 and 314 to different streams. Node312 also only receives, as input, an output of the node 310. Therefore,using the first rule, the system assigns node 312 to the same stream,i.e., stream 304, as the node 310.

As described above, streams are hardware queues whose operations areperformed in order. Thus, the order in which the Accelerator 302 assignsnodes to streams matters. The Accelerator 302 assigns nodes to streamsin an order of the direction of data flow in the subgraph. That is, theAccelerator 302 identifies one or more initial nodes of the subgraph andassigns the one or more initial nodes. Then, the Accelerator 302 followsdirected edges that are outputs of the one or more initial nodes toidentify subsequent nodes, and the Accelerator 302 assigns thesubsequent nodes to respective streams. The Accelerator 302 continuesassignment of nodes until each node in the subgraph is assigned. As aresult of assigning nodes in this order, operations within a givenstream will also be performed in the order in which the operations wereassigned, as described above. When the inputs of an operation A areproduced on different streams, it is necessary to ensure that they haveall been computed before operation A is executed. The execution on thestream to which operation A is assigned should be stalled until all ofthe inputs to operation A have been computed. The exact stallingmechanism is device specific. For GPU devices, an event can be createdfor each of the input streams and instructions can be added to eachstream to signal the event. For each input, an instruction can also beadded to the stream on which A is assigned in order for the operation towait for the relevant event in order to execute. In cases where one ormore of the inputs for operation A are computed on the same stream asoperation A, dataflow dependency instructions can be safely deleted,leading to better performance. Within a given stream, operationsrepresented by nodes assigned to the given stream that generate anoutput that is used as input by operations represented by one or moreother nodes assigned to the given stream will have been already computedor scheduled to be computed when the Accelerator 302 performs theoperations represented by the one or more other nodes.

Continuing with the illustration above, stream 304 is assigned node 310and then assigned node 312 because data flows from the node 310 to thenode 312. When executing operations in the stream, the Accelerator 302first executes operations represented by the node 310 and then executesoperations represented by the node 312.

After the final nodes, i.e., nodes 312 and 314, performs operations, theAccelerator 302 return the outputs of the nodes or an indication theoperations have completed to the system. In an example system, there isa special ‘send’ node that copies the computation results back from thememory of the Accelerator 302 into the host memory where it can behanded to a different device by a receive node or returned to the clientin a remote procedure call (RPC) response. The system can then, ifnecessary, return the output or the indication to the client.

Another implementation of assigning nodes to streams will be describedfurther below with reference to FIG. 4.

FIG. 4 is a flow diagram of an example process 400 for assigningsubgraphs to devices. For convenience, the process 400 will be describedas being performed by a system, e.g., a GPU. For example, a GPU canreceive instructions generated by a computational graph system, e.g.,the computational graph system 100 of FIG. 1, that, when executed, causethe GPU to perform the process 400.

The system can assign a particular node to a stream based on an amountof memory resources consumed by the node or by previously assignednodes. For example, the system can calculate a dimension of a tensor oneach directed edge to and from each node of the subgraph. The dimensionsof the tensors indicate a size of memory that would be consumed by adevice to perform an operation. The system may need to calculate alldimensions of a tensor in order to determine the size. The system canthen assign particular nodes with tensors consuming a particular size ofmemory to devices having the particular size of memory.

In particular, when the device performs the operation, the softwaredriver or executor allocates memory to store any inputs as well as anyoutputs computed as a result of the operation. Because the amount ofmemory on the device is limited, the device frees memory when memory isno longer used.

By way of illustration, the system determines whether an operationrepresented by a node has finished at a particular stream (step 402).For example, the system can periodically poll streams to determinewhether the operation in the particular stream has finished. The streammay support an action that allows the host to determine how farexecution has progressed through the list of operations in the stream.In some implementations, events, or markers, can signal how farexecution has progressed. When an event occurs, the event can be addedto a special hardware operation queue in the stream. The host can pollthis queue in order to determine which operations have occurred. Otherstream implementations may only allow the host to determine when allenqueued operations are complete. Alternatively or additionally, thehardware can provide an interrupt or callback when the stream reaches acertain point.

When the operation has finished, the system can determine memory usedfor inputs to the operation can be freed for use in other operations.The system does not free memory used for outputs of the operationbecause the outputs may be used in a subsequent node.

Thus, the system determines an amount of memory consumed that will befreed (step 404). The system can send a request to the software driveror executor to identify the size of memory that will be freed.

In some implementations, an example system allows the use of remotedirect memory access (RDMA) network interfaces that remote machines canuse to directly transfer data into the memory of a hardware acceleratorat an arbitrary point in time. This memory must not be in use by anyother operation running on any stream. The example system may not needto know precisely how far operations on each stream has progressed.However, the system should keep track of memory known not to be in useby any stream. This free memory can then be used for RDMA.

The system determines, for each of a group of unassigned nodes, arespective estimated amount of memory consumed by the unassigned node(step 406). The unassigned nodes can include nodes that receive inputsfrom the node whose operation has completed. The unassigned nodes canalso include nodes that are independent from the node whose operationhas completed but still need to be processed by the accelerator. Theestimated amount of memory can be determined by evaluating dimensions ofthe respective tensors to the unassigned nodes, as described above.

The system determines, from the group of unassigned nodes, a firstunassigned node that represents an operation, which when executed on astream by the accelerator, maximizes usage of the amount of memory thatwill be freed (step 408). If an operation represented by an unassignednode requires more memory to execute than the amount of memory that willbe free, the unassigned node will not be assigned to the stream. If afirst and second operation require a respective estimated amount ofmemory less than or equal to the amount of memory that will be free, thesystem selects the operation that maximizes usage of the amount ofmemory that will be freed. In other words, in this case, the systemdetermines the node representing the selected operation as the firstunassigned node. An example system does not enqueue an operation on thestream until it can determine which regions of accelerator memory willbe used to hold the temporary working space and outputs of theoperation. In the event that memory is scarce, an example system maychoose to enqueue operations that require smaller amounts of memory toexecute or to preferentially enqueue operations that will consume largeinput tensors allowing them to be deallocated.

The system assigns an operation represented by the first unassigned nodeto the particular stream (step 410). The system can then cause theparticular stream to perform the operation, and the system can continueoperating as described above with reference to FIGS. 2-3.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non-transitory program carrier for execution by, or to controlthe operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on anartificially-generated propagated signal, e.g., a machine-generatedelectrical, optical, or electromagnetic signal, that is generated toencode information for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them. The computer storage medium is not, however, apropagated signal.

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, or multiple processors or computers.The apparatus can include special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application-specificintegrated circuit). The apparatus can also include, in addition tohardware, code that creates an execution environment for the computerprogram in question, e.g., code that constitutes processor firmware, aprotocol stack, a database management system, an operating system, or acombination of one or more of them.

A computer program (which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code) can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub-programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.

As used in this specification, an “engine,” or “software engine,” refersto a software implemented input/output system that provides an outputthat is different from the input. An engine can be an encoded block offunctionality, such as a library, a platform, a software development kit(“SDK”), or an object. Each engine can be implemented on any appropriatetype of computing device, e.g., servers, mobile phones, tabletcomputers, notebook computers, music players, e-book readers, laptop ordesktop computers, PDAs, smart phones, or other stationary or portabledevices, that includes one or more processors and computer readablemedia. Additionally, two or more of the engines may be implemented onthe same computing device, or on different computing devices.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Computers suitable for the execution of a computer program include, byway of example, can be based on general or special purposemicroprocessors or both, or any other kind of central processing unit.Generally, a central processing unit will receive instructions and datafrom a read-only memory or a random access memory or both. The essentialelements of a computer are a central processing unit for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto-optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer-readable media suitable for storing computer programinstructions and data include all forms of non-volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto-optical disks; andCD-ROM and DVD-ROM disks. The processor and the memory can besupplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) monitor, an LCD(liquid crystal display) monitor, or an OLED display, for displayinginformation to the user, as well as input devices for providing input tothe computer, e.g., a keyboard, a mouse, or a presence sensitive displayor other surface. Other kinds of devices can be used to provide forinteraction with a user as well; for example, feedback provided to theuser can be any form of sensory feedback, e.g., visual feedback,auditory feedback, or tactile feedback; and input from the user can bereceived in any form, including acoustic, speech, or tactile input. Inaddition, a computer can interact with a user by sending resources toand receiving resources from a device that is used by the user; forexample, by sending web pages to a web browser on a user's client devicein response to requests received from the web browser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back end, middleware, or front end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or of what may be claimed, but rather as descriptions offeatures that may be specific to particular embodiments of particularinventions. Certain features that are described in this specification inthe context of separate embodiments can also be implemented incombination in a single embodiment. Conversely, various features thatare described in the context of a single embodiment can also beimplemented in multiple embodiments separately or in any suitablesubcombination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In certain implementations, multitasking and parallelprocessing may be advantageous.

What is claimed is: 1-40. (canceled)
 41. A computer program productencoded on one or more non-transitory computer storage media, thecomputer program product comprising instructions that, when executed bya system comprising a plurality of hardware streams, cause the system toperform program operations comprising: for each of a plurality ofoperations represented in a computational graph, assigning the operationto a respective stream in the plurality of streams of the system, eachstream configured to queue operations assigned to the stream and toexecute the queued operations in a defined order on a respectivehardware resource for the stream; configuring a first stream of theplurality of streams to stall performance of a first operation assignedto the first stream until all inputs to the first operation have beencomputed, wherein a first input to the first operation comprises anoutput of a second operation assigned to a second, different stream ofthe plurality of streams; and performing, by each stream in theplurality of streams, the operations that were assigned to the stream ina defined order, including performing at least one operation by thefirst stream in parallel with at least one operation by the secondstream.
 42. The computer program product of claim 41, the programoperations further comprising: receiving, from a client, a requestidentifying one or more particular outputs from one or more operationsrepresented in the computational graph; and providing the one or moreparticular outputs to the client.
 43. The computer program product ofclaim 41, the program operations further comprising: receiving data thatidentifies a group of operations represented in the computational graphthat are connected to each other by following one directed edge fromoperation to operation represented in the computational graph; andassigning the group of operations to one stream.
 44. The computerprogram product of claim 41, wherein the assigning comprises: receivingdata identifying a representation of a first operation in thecomputational graph having a plurality of directed edges as outputs; andassigning, for each of the directed edges, a target operation to whichthe directed edge points to a unique hardware stream of the system, eachtarget operation being assigned to a different unique hardware stream.45. The computer program product of claim 41, the program operationsfurther comprising determining, for each of a plurality of nodes in thecomputational graph that represent respective ones of the plurality ofoperations, a respective amount of memory resources consumed by theoperation represented by the node based on information about directededges to the node, wherein assigning the operation represented by eachnode in the computational graph to a respective hardware stream is basedat least on the respective amount of memory resources consumed by theoperation represented by the node.
 46. The computer program product ofclaim 41, the program operations further comprising: determining aparticular operation represented represented in the computational graphhas finished at a particular hardware stream; in response to determiningthe particular operation has finished, determining a first amount ofmemory consumed by the particular operation that will be freed;determining, for each of a group of unassigned operations, a respectiveestimated amount of memory that will be consumed by the unassignedoperation; determining, from the group of unassigned operations andusing the respective estimated amount of memory that will be consumed bythe unassigned operation, a first unassigned operation with theestimated amount of memory that maximizes usage of the first amount ofmemory; and based on determining that the first unassigned operationmaximizes usage of the first amount of memory, assigning the firstunassigned operation to the particular hardware stream.
 47. The computerprogram product of claim 42, the program operations further comprisingcausing the system to store the one or more particular outputs in memoryof a hardware accelerator.
 48. The computer program product of claim 41,the program operations further comprising: determining that a particularoperation represented assigned to a particular hardware stream hasfinished execution; and in response to determining that the particularoperation has finished execution: identifying at least one subsequentoperation that uses the output of the particular operation as input, andreusing memory allocated for the output of the particular operationafter the at least one subsequent operation has executed.
 49. Thecomputer program product of claim 41, wherein assigning each operationin the computational graph to a respective stream in the plurality ofstreams comprises assigning operations so as to minimize a number ofcross-stream directed edges, wherein a cross-stream directed edge is aninstance of an input to an operation in one stream being received froman output of an operation in another stream.
 50. The computer programproduct of claim 41, wherein performing the operations represented bythe nodes in the computational graph comprises: identifying, at a pointimmediately preceding performance of the first operation in the firststream, that the output of the second operation assigned to the secondstream has not yet been computed; and stalling performance of the firstoperation in the first stream until the output of the second operationsfrom the second stream is available as input to the first operation inthe first stream.
 51. The computer program product of claim 50, whereinstalling performance of the first operation in the first stream furtherstalls performance of additional operations downstream of the firstoperation in the first stream.
 52. The computer program product of claim41, wherein the computational graph is a subgraph corresponding to aportion of a larger computational graph.
 53. A method performed by asystem comprising a plurality of hardware streams, comprising: for eachof a plurality of operations represented in a computational graph,assigning the operation to a respective stream in the plurality ofstreams of the system, each stream configured to queue operationsassigned to the stream and to execute the queued operations in a definedorder on a respective hardware resource for the stream; configuring afirst stream of the plurality of streams to stall performance of a firstoperation assigned to the first stream until all inputs to the firstoperation have been computed, wherein a first input to the firstoperation comprises an output of a second operation assigned to asecond, different stream of the plurality of streams; and performing, byeach stream in the plurality of streams, the operations that wereassigned to the stream in a defined order, including performing at leastone operation by the first stream in parallel with at least oneoperation by the second stream.
 54. The method of claim 53, comprising:receiving, from a client, a request identifying one or more particularoutputs from one or more operations represented in the computationalgraph; and providing the one or more particular outputs to the client.55. The method of claim 53, comprising: receiving data that identifies agroup of operations represented in the computational graph that areconnected to each other by following one directed edge from operation tooperation represented in the computational graph; and assigning thegroup of operations to one stream.
 56. The method of claim 53, whereinthe assigning comprises: receiving data identifying a representation ofa first operation in the computational graph having a plurality ofdirected edges as outputs; and assigning, for each of the directededges, a target operation to which the directed edge points to a uniquehardware stream of the system, each target operation being assigned to adifferent unique hardware stream.
 57. The method of claim 53, comprisingdetermining, for each of a plurality of nodes in the computational graphthat represent respective ones of the plurality of operations, arespective amount of memory resources consumed by the operationrepresented by the node based on information about directed edges to thenode, wherein assigning the operation represented by each node in thecomputational graph to a respective hardware stream is based at least onthe respective amount of memory resources consumed by the operationrepresented by the node.
 58. The method of claim 53, comprising:determining a particular operation represented in the computationalgraph has finished at a particular hardware stream; in response todetermining the particular operation has finished, determining a firstamount of memory consumed by the particular operation that will befreed; determining, for each of a group of unassigned operations, arespective estimated amount of memory that will be consumed by theunassigned operation; determining, from the group of unassignedoperations and using the respective estimated amount of memory that willbe consumed by the unassigned operation, a first unassigned operationwith the estimated amount of memory that maximizes usage of the firstamount of memory; and based on determining that the first unassignedoperation maximizes usage of the first amount of memory, assigning thefirst unassigned operation to the particular hardware stream.
 59. Themethod of claim 54, comprising causing the system to store the one ormore particular outputs in memory of a hardware accelerator.
 60. Asystem comprising: a plurality of hardware streams; and one or morenon-transitory computer storage media encoded with instructions that,when executed, cause performance of operations comprising: for each of aplurality of operations represented in a computational graph, assigningthe operation to a respective stream in the plurality of streams of thesystem, each stream configured to queue operations assigned to thestream and to execute the queued operations in a defined order on arespective hardware resource for the stream; configuring a first streamof the plurality of streams to stall performance of a first operationassigned to the first stream until all inputs to the first operationhave been computed, wherein a first input to the first operationcomprises an output of a second operation assigned to a second,different stream of the plurality of streams; and performing, by eachstream in the plurality of streams, the operations that were assigned tothe stream in a defined order, including performing at least oneoperation by the first stream in parallel with at least one operation bythe second stream.